Today in this lecture, we are going to learn about the methods for Measurement of Op Amp Parameters. We already learned about the op-amp in very detail. You can learn the op-amp from the below link.

Also Read:what is Op-amp? | Block diagram of op-amp

## Measurement of Op Amp Parameters

In this section, we are going to learn the methods to measure the following op-amp parameters.

Op-Amp Parameters | |
---|---|

1. | Open loop voltage gain |

2. | Differential input resistance |

3. | Output resistance |

4. | Input bias current |

5. | CMRR |

6. | Input offset current |

7. | Output offset voltage |

8. | Power supply rejection ratio (PSRR) |

9. | Power supply rejection ratio (PSRR) |

10. | Input offset Voltage |

Now we will see the methods to find each parameter of op-amp in detail.

## Open Loop Voltage Gain

The open loop voltage gain is the ratio of the output signal to the input differential signal V_{d}. Note that the feedback is not introduced and the op-amp is operating in the open loop mode.

**Measurement Procedure:**

- Apply +V
_{CC}and -V_{CC}. - Connect the signal generator and adjust Vs in order to get maximum undistorted output at 1KHz frequency.
- Measure V
_{o}and V_{d}and calculate the open loop voltage gain as \mathbf{A_v = \frac{V_o}{V_d}} - The resistance connected at the non-inverting (+) terminal of the op-amp is used to nullify the effect of the offset voltage.

## Differential Input Resistance

The circuit diagram for measuring the differential input resistance is shown in the below figure.

**Measurement Procedure:**

- Connect equal value resistance each of value R to each input terminal as shown in the above figure.

- From the above figure, assuming the input resistance as R
_{i},

\mathbf{V'_i = V_i \left[ \frac{R_i}{2R + R_i}\right ]}

- The corresponding output voltage V’
_{0}is given by,

\mathbf{V'_0 = A_v.V'_i = A_v. \left[ \frac{R_i}{2R + R_i}\right ]V_i}

Where, A_{v} = Open loop gain

- Now remove both the resistors and apply V
_{i}directly to the op-amp. The corresponding output voltage V_{o}is given by,

\mathbf{V_o = A_v . V_i}

- From the above, divide V’
_{o}by V_{o}to get,

\mathbf{\frac{V'_o}{V_o} = \frac{R_i}{R_i + 2R}}

- Rearranging the above equation, we will get,

\mathbf{R_i= 2R \left[ \frac{V'_o}{V_o - V'_o}\right ]}

Thus by measuring V_{o} and V’_{o}, we can measure the differential input resistance.

## Input Bias Current

The input bias current is the average of the currents that flow into the inverting and non-inverting input terminals.

As already defined, \mathbf{I_B = \frac{I_{B1}+I_{B2}}{2}}. The measurement setup is shown in the figure below.

The resistance R is of very high value (a few MÎ©). The capacitors C_{1} and C_{2} are connected across them in order to bypass any noise present.

**Measurement Procedure:**

- Short the terminal C and D. Thus point C will be connected to ground. As per the virtual ground concept, point A also will be at ground potential.

\mathbf{V_{o1}=I_{B1}R \,} or \mathbf{I_{B1} = V_{o1}/R}

So measure V_{o1} to calculate I_{B1}.

- Now Short the terminals A and B. Thus A and B are equipotential points. Point C is also at the same potential as A due to the virtual ground.

V_{A} = V_{B} = V_{C} = V_{o2}

But, V_{C} = I_{B2} R_{2}

V_{o2} = I_{B2} R , I_{B2} = V_{o2} / R

Once I_{B1} and I_{B2} are measured, we can obtain the value of I_{B}.

## Input Offset Current

The setup of measurement of the input offset current is the same as that for the input bias current (refer to the below figure). Measure I_{B1} and I_{B2} and calculate input offset current Iios as

\mathbf{I_{ios} = \left | I_{B1} - I_{B2} \right |}

## Input Offset Voltage

Input offset voltage V_{ios} is defined as the voltage that must be applied between the input terminals in order to get a zero output voltage. The experimental circuit to measure V_{ios} is shown in the below figure.

Looking at the above figure, we can write that,

\mathbf{I = \frac{V_o - V_{ios}}{R_F}}

and, \mathbf{V_{ios} = IR_1}

\therefore \mathbf{V_o = IR_F + V_{ios} = \frac{V_{ios}}{R_1}\times R_F + V_{ios}}

\therefore \mathbf{V_o = V_{ios}\left [ 1 + \frac{R_F}{R_1} \right ]}

Thus V_{ios} can be calculated by measuring V_{o} and selecting the resistor R_{F} and R_{1} properly.

## Measurement Of CMRR

CMRR is the ratio of differential gain A_{d} to the common mode gain A_{c}.

V_{o} = A_{d} V_{d} and V_{o} = A_{c} V_{c}

Where, V_{d} = Differential input signal, V_{c} = Common mode input signal

\mathbf{CMRR = \frac{A_d}{A_c} = \frac{V_o/V_d}{V_o/V_c} = \frac{V_c}{V_d}}

Measurement of CMRR is based on the above equation. The setup for CMRR measurement is shown in the below figure.

Looking at the above figure, we can write that,

\mathbf{V_c = V_s\left[\frac{R_2}{R_1 + R_2}\right ]}

But as R_{2} = R_{F},

\mathbf{V_c = V_s\left[\frac{R_F}{R_1 + R_F}\right ] = V_s\left [ 1+\frac{R_F}{R_1} \right ]}

Also, the output voltage V_{o} is given by,

\mathbf{V_o = V_d\left [ 1+\frac{R_F}{R_1} \right ]}

From the above equations, it is possible to obtain the values of V_{c} and V_{d} and calculate CMRR.

Also Read:Methods to improve CMRR

## Output Offset Voltage

The output offset voltage is defined as the difference between t DC voltages present at the output terminals when both the input terminals are connected to the ground. The output offset voltage is present due to two factors:

- Due to the input offset voltage V
_{ios} - Due to the input bias current I
_{B}

The experimental circuit used to measure the output offset voltage due to the input bias current is shown in the below figure.

**Measurement Procedure:**

I_{B1} and I_{B2} are very small currents flowing into the two input terminals of op-amp/ The output voltage produced only due to I_{B2} is given by,

**V _{o1} = – I_{B2} R_{F}**

The output produced only due to I_{B1} is given by,

\mathbf{V_{o2} = I_{B1}R_2\left [ 1 + \frac{R_F}{R_1} \right ]}

For all practical circuits R_{2} = R_{1}. Hence,

\mathbf{V_{o2} = I_{B1}R_1\left [ 1 + \frac{R_F}{R_1} \right ] = I_{B1}[R_1 + R_F]}

Output offset voltage due to the input bias currents I_{B1} and I_{B2} is given by,

**V _{o1} + V_{o2} = – I_{B2} R_{F} + I_{B1} R_{F} + I_{B1} R_{1}**

If we select R_{F} >>R_{1} then we can neglect the last term in the above equation to write

**V _{o1} + V_{o2} = R_{F} (I_{B1} – I_{B2})**

But I_{B1} – I_{B2} = I_{ios} = Input offset current

**âˆ´ V _{o1} + V_{o2} = I_{ios} R_{F}**

The output offset voltage due to the input offset voltage Vios is given as, I_{ios} [1 + (R_{F} / R_{i})].

Therefore the total output offset voltage is given by,

\boxed{\mathbf{V_{oos} = I_{ios}[1 +(R_F/R_i)]+I_{ios}R_F}}

## Output Resistance

It is the resistance measured between the output terminal and the ground. The experimental setup used to measure the output resistance is shown in the below figure.

**Measurement Procedure:**

Keep the short link between A and B open. Apply input V_{i} to the non-inverting terminal and measure the output voltage.

**V _{o} = V_{i} [1 + (R_{F}/R_{1})] = A_{F} V_{i}**

Where A_{F} = The closed loop gain of Op-amp

Now connect the short link between A and B. Adjust the input voltage V_{i} and V’_{i} in order to get the same output voltage V_{o}. Let the closed-loop gain at this time be A’_{F}.

**V _{o} = A’_{F} V’_{i}**

The amplifier equivalent circuit when A and B are short-circuited is also shown in the above figure. From the figure we can write,

\mathbf{V_o = \frac{R_L}{(R_o + R_L)} \times A_F V_i}

But, \mathbf{V'_i = \frac{V_O}{A'_F}}

\therefore \mathbf{V_o = \frac{A_F[V_O/A'_F]}{(R_o + R_L)} \times R_L}

\therefore \mathbf{\frac{A_F}{A'_F} = \frac{R_o + R_L}{ R_L}}

Simplifying the expression we get,

\therefore \mathbf{R_o = R_L \left [ \frac{A_F}{A'_F} - 1\right ]}

## Power Supply Rejection Ratio (PSRR)

The experimental setup used for the measurement of PSRR is shown in the below figure.

**Measurement Procedure:**

Adjust the potentiometer P to obtain a zero output voltage. This voltage V_{2} in the figure is nothing but the input offset voltage V_{ios}.

\therefore \mathbf{V_{ios} = V_2 = \frac{R_2}{R_1 + R_2} \times V_1}

Let us select R_{2} << R_{2} hence,

\therefore \mathbf{V_2 = \left [ \frac{R_2}{R_1} \right ]V_1 = V_{ios}}

Keep V_{EE} constant and change V_{CC} by Î”V_{CC} and measure the corresponding change in V_{2} i.e. Î”V_{2}. But Î”V_{2} is nothing but Î”V_{ios}.

\therefore \mathbf{PSRR = \frac{\Delta V_{ios}}{\Delta V_{cc}}}

## Slew Rate

As already defined, the slew rate is the maximum rate of change of output voltage with time. it is specified in V/Î¼S. The circuit used for slew rate measurement is shown in the below figure. The non-inverting configurations are being used because it has the worst (smallest) value of the slew rate.

Note that a square wave is applied at the non-inverting terminal of op-amp.

The frequency of this square wave signal is increased gradually till we get a distorted output voltage. The distortion can be observed on the CRO.

The input and output voltage waveforms are also shown in the figure.

The slew rate is then measured from the output voltage waveforms as:

\mathbf{Slew\,Rate = \frac{\Delta V_{ios}}{V_{cc}}}

Ideally, the slew rate should be infinite and practically it should be as large as possible.

You can also read the full lecture on the Slew rate link given below.

Also Read:Slew Rate of Op Amp